How to tell my mentor to be careful when discussing my work in progress around people I do not trust?

If you can trust your mentor, just tell them. Say it as it is. But not in an email. This requires personal communication.

But, if you cannot trust your mentor then you have a bigger problem than you state and need to find better guidance.

As a meta comment, sharing your research is on average the best way to progress in my opinion. Sure, there are some bad apples out there, but overall I feel it’s wise to err on the side of collaboration and communication.

I suggest that my students prepare human readable manuscripts that they can share with others. No one stole their work yet (though it did happen to me once). Again, on average this is better I think.

To your question: I think directly and politely asking is the best way. “Hi, I feel like the work is not quite ready to be discussed as it’s too preliminary, would it be ok if we develop it more before we present it? I feel it would have more impact this way”

Don’t mention distrust or plagiarism. If your professor is not completely dense they’d understand that this is part of it.

Good luck!